Paramagnetic shimming for wide-range variable-field NMR.

TL;DR: This work proposes a new passive shimming strategy for variable-field NMR experiments, in which the magnetic field produced by paramagnetic shim pieces placed inside the magnet bore compensates the inhomogeneity of a variable- field magnet for a wide range of magnet currents.

Abstract: We propose a new passive shimming strategy for variable-field NMR experiments, in which the magnetic field produced by paramagnetic shim pieces placed inside the magnet bore compensates the inhomogeneity of a variable-field magnet for a wide range of magnet currents. Paramagnetic shimming is demonstrated in 7 Li, 87 Rb, and 45 Sc NMR of a liquid solution sample in magnetic fields of 3.4, 4.0, and 5.4 T at a fixed carrier frequency of 56.0 MHz. Since both the main-field inhomogeneity and the paramagnetic magnetization are proportional to the main-magnet current, the resonance lines are equally narrowed by the improved field homogeneity with an identical configuration of the paramagnetic shim pieces. Paramagnetic shimming presented in this work opens the possibility of high-resolution variable-field NMR experiments.

Summary

1 Introduction

• High-resolution nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) experiments require a strong, stable, and homogeneous magnetic field over the sample volume.
• There, little attention has been paid to the field homogeneity, as the line-broadening effect is masked by the intrinsic linewidth.
• Indeed, the variable-field superconducting magnets are widespread for use in various scientific research fields, but not in NMR for chemical analysis where the requirement for the homogeneity is so demanding.
• In principle, both the electric and ferromagnetic shimming schemes are expected to work by changing the currents or configuration every time the magnetic field is altered.
• Instead of the ferromagnetic steel pieces, the authors employ pieces of paramagnetic material.

2 Strategy

• The idea of passive shimming is to place a number of magnetic pieces so that the net magnetic field they produce cancels the original field inhomogeneity.
• Given knowledge about the field profile the authors want to correct, the configuration of the shim pieces can be obtained by solving Eq. (1) numerically.
• Figure 1(d) shows re-measured field distribution along the capillary axis, which seemed to be slightly tilted from the z-axis of the stage used to obtain the data in Fig. 1(b) and (c). Figure 1(e) shows a histogram representing the resonance frequency distribution, which indicates asymmetric line broadening over ca. 540 ppm due to the field inhomogeneity.
• Even though both are known to obey Curie’s law, the rare earth ions show some preferable features.
• In general, agreement between the theoretical and measured effective Bohr magneton is excellent[7].

3 Results and discussion

• The sample was doped with manganese (II) chloride to shorten spin–lattice relaxation times and was put into the capillary with an inner diameter of 1.0 mm.
• The volume susceptibility χv of the paramagnetic shim pieces was adjusted by diluting Dy2O3 with KBr, whose susceptibility was measured to be negligible compared to that of Dy2O3.
• The authors made a pair of pellets with the optimized radius and height of 9.0 and 6.3 mm, respectively.
• It presumably explains the result that the optimal d (6.7 and 7.2 mm) was smaller than the predicted value (8.63 mm).

Figures

Fig. 5. A result of SQUID measurements of Dy2O3 showing field (B) dependence of the magnetic flux. The mass susceptibility χg is given by the slope of the solid line obtained by least-square fitting to be 3.09 mm3g−1. The coefficient of determination was 0.99999513 (1-4.87×10−6)

Fig. 6. A snapshot of the probehead composed of a tuned saddle coil and a pair of paramagnetic pellets. Their vertical positions can be adjusted independently.

Fig. 3. Calculated field profiles with (solid line) and without (broken line) the shim pellets for R = 9.00 mm, d = 8.63 mm, t = 6.30 mm, and χv = 0.0139.

Fig. 2. A configuration of a pair of paramagnetic shim pellets with a radius R and a thickness t. d is the distance between the inner face of the pellets and the origin (z = 0). χv represents the volume magnetic susceptibility.

Fig. 7. 7Li, 87Rb, and 45Sc spectra obtained using the paramagnetic shim pellets with the optimized configuration. For comparison, the spectra obtained without shimming are shown in the gray lines. The number of scans was 8000 for each spectrum.

Fig. 1. (a) A snapshot of a cryogen-free superconducting magnet (mCFM-7T-50-H3, Cryogenic Ltd.). (b) Measured field distribution determined from the 1H resonance frequency of paraffin in a microcoil with an inner diameter of 0.4 mm. Measurements were performed over 847 positions of the microcoil with x- and y-intervals of 0.5 mm and a z-interval of 1 mm. The carrier frequency was 82 MHz and the magnet current was 20.5 A. x-, y-, and z-dependences of the magnetic field are plotted in (c) with circles, triangles, and squares, respectively. (d) Field distribution along the capillary sample tube. Using a microcoil with a coil diameter of 0.1 mm, 1H NMR signals of glycerol were measured for various positions by sliding the microcoil inside the empty capillary. The solid line is a fitted curve of the experimental data (squares) using a quadratic function (see Eq. (3)). The magnet current was set to 36.1 A, and the carrier frequency was 56.0 MHz. (e) A histogram of resonance frequency distribution over a range of −4 ≤ z ≤ 4 mm.

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The authors propose a new passive shimming strategy for variable-field NMR experiments, in which the magnetic field produced by paramagnetic shim pieces placed inside the magnet bore compensates the inhomogeneity of a variable-field magnet for a wide range of magnet currents. Paramagnetic shimming presented in this work opens the possibility of high-resolution variable-field NMR experiments.